calculation of contour integral
We will determine the important complex integral
I:= |
where is the circumference of the circle taken anticlockwise and an arbitrary integer.
Let’s take the “direction angle” of the radius of as the parametre , i.e.
Then on , we have
and
whence
In the case one gets trivially . If , we obtain
using the fact that is a period of the exponential function (http://planetmath.org/PeriodicityOfExponentialFunction).
Hence we can write the result
Title | calculation of contour integral |
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Canonical name | CalculationOfContourIntegral |
Date of creation | 2013-03-22 19:14:16 |
Last modified on | 2013-03-22 19:14:16 |
Owner | pahio (2872) |
Last modified by | pahio (2872) |
Numerical id | 8 |
Author | pahio (2872) |
Entry type | Example |
Classification | msc 30E20 |
Classification | msc 30A99 |
Related topic | AntiderivativeOfComplexFunction |
Related topic | SubstitutionNotation |
Related topic | ProofOfCauchyIntegralFormula |